4. We say that a vector field F(x, y) is conservative on a domain D if it is the gradient of some potential function f(x, y) defined on D. Let F(x, y) = (zzyz' 72tyz. (a) [2 points] Let C be the circle of radius 1 centered at (2, 2). Show that F is conservative inside C by finding a potential function that is defined on the interior of C. (b) [2 points] Now instead let C be the positively oriented unit circle. Give a geometric argument which shows that ,F . dr = 27. If you are unable to find a geometric solution, you can solve the integral directly for half marks. (c) [2 points] Use the conclusion of part (b) to explain why F cannot be conservative inside the unit circle. (d) [2 point] Explain why the potential function you found in part (a) fails to be a potential function inside the unit circle